You can't divide by zero, but no one can actually prove WHY. . . I wanted
to see a real proof first. . . We learned in trig that you can't raise
zero to the zero-th power because zero would equal one, obviously. I
realize infinity is not so much a number as an endless amount, but if
there are an infinite number of numbers between 1 and 2, and an infinite
number of numbers between 1 and 50, wouldn't the second infinity be
bigger than the first?

Divide a line segment into three parts, one half and one a quarter the
length of the line segment. Choose a point at random along this line
segment. What is that probability that this point lands in the 1/2
segment...?

When I learned how to convert repeating decimals to fractions, we were
given an example in which .9 repeating equalled one. The problem I have
is that I can't logically believe this is true, and I don't see an error
with the math, so what am I missing or forgetting to resolve this?

I want to know how to explain the Intermediate Value Theorem in its
most simple form: If f is a continuous function on the closed interval
[a,b] and N is any number between f(a) and f(b), there must be a
number c in (a,b) such that f(c)= N.